Question

The sum of three consecutive odd number is 38 more then the average of these numbers

Answer 1

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Answer 2

$\huge{\bf{\underline{\pink{Solution :}}}}$

$\implies$Suppose the three  Consecutive Odd number be - a + 1 , a + 3 , a + 5

$\mapsto \underline{\sf{\pink{According \ to \ the \ Question :}}}$

• The sum of three consecutive odd number is 38 more then the average of these numbers.

$\implies \sf{a + 1 + a + 3 + a + 5 = \dfrac{a + 1 + a + 3 + a + 5}{3} + 38}$

$\implies \sf{3a + 9 = \dfrac{3a + 9}{3} + 38}$

$\implies \sf{3a + 9 = \dfrac{3a + 9 + 114}{3}}$

$\implies \sf{3a + 9 = \dfrac{3a + 123}{3}}$

$\implies \sf{9a + 27 = 3a + 123}$

$\implies \sf{9a - 3a = 123 - 27}$

$\implies \sf{6a = 96}$

$\implies \sf{a = \dfrac{96}{6}}$

$\implies \boxed{\sf{a = 16}}$

Therefore,

$\implies \boxed{\bold{\red{First \ Number = a + 1 = 16 + 1 = 17}}}$

$\implies \boxed{\bold{\red{Second \ Number = a + 3 = 16 + 3 = 19}}}$

$\implies \boxed{\bold{\red{Third \ Number = a + 5 = 16 + 5 = 21}}}$

$\rule{200}2$